text:
Did John Stringfellow ever build an aeroplane, powered by a steam engine, that really flew?
After doing some research, I found two apparently conflicting articles. The first, dated Sep. 23, 1848, describes John Stringfellow as marching through the air in a tent. The second, published about 20 years later (July 10, 1868) quotes Stringfellow as declaring that the world still waited to see him flying.
Question: Did John Stringfellow ever build an aeroplane, powered by a steam engine, that really flew? Does it exist written contemporary evidence (letters, articles, patents, etc.) proving that this inventor designed, built and flew a plane of any kind (manned or just a model)?
1848-09-23, Scientific American, September 23, 1848, col. 3, p. 4.

An Air Navigator.
A series of experiments have lately been made beneath an immense tent
in Cremorne Gardens, London, by a Mr. Stringfellow — a fine name for
suspension. The inventor marches through the air by a machine which
sustains and propels itself through the cicumambient fluid. The
machine excited considerable attention and surprised all the
spectators by its wonderful performance. The next expedition that is
fitted out by the British government to explore the Niger and the
country through which it winds its sluggish and pestilential way,
should employ this Mr. Stringfellow with a number of his machines to
make a flying exploration, untramelled with their heels in mud or
water.

1868-07-10, "Aerial Navigation", English Mechanic and Mirror of Science, July 10, 1868, col. 3, p. 341.

Aerial Navigation ...
Mr. Stringfellow, one of the exhibitors at the Crystal Palace,
enthusiastically declared that the world should yet see that he could
fly with his own machine, and this opinion seemed to be universally
held. ...

I think this should be on Skeptics.SE. While it relates to flight, it's more about debunking claims and suited to that site. That being said, if there were definitive proof it would be quite the publicized story, given that the Wright brothers are (largely) credited with the first manned flight. If that happened 50+ years prior, we should have good reporting on that.

@RonBeyer, Attention! John Stringfellow is not really in conflict with the Wright brothers but with Alphonse Penaud, Victor Tatin and Langley himself, because all these three inventors built model planes that flew. My question refers to "a plane of any kind" not necessarily to one that was able to carry a person.

Re - "My question refers to "a plane of any kind" not necessarily to one that was able to carry a person. –" -- you should edit to clarify that.  The quotes about "marching through the air in a tent" and " The inventor marches through the air" strongly imply that you are talking about manned flight.

@quietflyer ,  I added the clarification :"a plane of any kind (manned or just a model)".

Let's put it this way: Had Stringfellows 1848 experiment succeeded, wouldn't he had tried to repeat it at the 1868 exhibition? The way things developed clearly indicates that his experiment discouraged him from further developing flying machines and only later cock-and-bull stories make us think today he might have succeeded. The same is true for Cayley and all the other pioneers. The first serious success was only achieved by Penaud.

I was not able to discover articles of 1848, or even up to 5 years after, that give details about the 1848 flight of Stringfellow's model. However, I found 3 first hand articles, published on July 3, 24 and Oct. 9, 1868, which say that, at an exhibition which took place starting with June 25, 1868, at the Crystal Palace in London, John Stringfellow exhibited two engines. For the larger one, that generated, when started, a little more than 1 HP, he took a prize of 100 pounds. The smaller motor was installed on a working plane which apparently flew but the description is vague being unclear whether the author talks about an event that happened in 1868 or he refers to previous flights, like the one of 1848. Anyway, the conclusion was that despite taking the prize (for the larger standalone engine) it was not clear whether that motor would serve for any practical purposes in aeronautics.
From the numerical values furnished by the commission that awarded the prize, it results that Stringfellow's motor needed:
$150 ft * 3 in^2 = 88.5 liters$ of steam at $80 lbf/in^2 = 5.4 atm$ per minute to generate 1.09 HP continuous power.
Nothing is said about the interval of time during which the boiler was able to maintain this considerable flow of steam. Another remark would be that the steam was expelled from the cylinder at 5.4 atm which means the engine had a very poor efficiency.
"The Aeronautical Society of Great Britain", The Mechanics' Magazine, July 3, 1868, col. 2-3, p. 3.

THE AERONAUTICAL SOCIETY OF GREAT BRITAIN. ...
We have said that there are a few exhibits which are a step in advance
of the rest at the Crystal Palace. Amongst the rest may be noticed a
working model of an aerial steam carriage, by Mr. J. Stringfellow, the
whole, including engine, boiler, water and fuel, weighing about 12
lb.; cylinder, 1 3-16ths inch diameter; 2-inch stroke; works two
propellers, 21 in. diameter, about 600 revolutions per minute; gets up
steam of 100 lb. pressure in five minutes. ...

"The Aeronautical Society Late Exhibition", English Mechanic and Mirror of Science, July 24, 1868, col. 3, p. 378.

THE AERONAUTICAL SOCIETY'S LATE EXHIBITION.
THOSE who predicted that the exhibition of the Aeronautical Society at
the Crystal Palace would prove a failure may, in part be said to have
been true prophets; but the exhibition was not all a failure — far
from it: enough, we think, was given in evidence to cause at least one
section of the members to be of good heart. True, the expected
demonstration of the possibility of flying was not made, and the
rewards offered for flying have not been gained. The flying man put in
no appearance with bis wings, and the only model of this class which
actually worked was the ingenious steam-propelled machine of Mr.
Stringfellow, which, running along a a wire, has enabled our facetious
contemporary, "Punch," to change the inventor's name to Wirefellow,
and which elicited the remark from sundry spectators of a certain
class that "he was wiring into it."

"The Aeronautical Exhibition", The Mechanics Magazine, October 9, 1868, pp. 282-284.

THE AERONAUTICAL EXHIBITION.
IT will be fresh in the memory of our readers that the Aeronautical
Society of Great Britain held their first exhibition at the Crystal
Palace on the 25th of June last and ten following days. ...
The only engines, therefore, which competed for the prize were three,
— one by M. Camille Vert and two by Mr. J. Stringfellow. M. Vert's
engine was a small model of a steam engine, weighing 2 lb., for
propelling a hydrogen gas balloon. Mr. Stringfellow's engine No. 1 was
a light engine and boiler for aerial purposes; it was of 1-horse
power, and weighed 13 lb. No. 2 was a similar engine on a smaller
scale. M. Vert's engine was found to be too small to enable any
accurate test to be applied for ascertaining its power. The jurors
state that it appeared to keep up steam well in the repeated
demonstrations in propelling a model balloon in various directions
within the Crystal Palace building.
Mr. Stringfellow's engine No. 1, from its size and power, may be
considered something more than a mere model. The cylinder was 2 in. in
diameter, stroke 3 in., and it worked with a boiler pressure of 100
lb. per square inch, the engine making 300 revolutions per minute. The
time of getting up steam was noted; in three minutes after lighting
the fire, the pressure was 30 lb., in five minutes 50 lb., and in
seven minutes there was the full working pressure of 100 lb. When
started, the engine had a fair amount of duty to perform in driving
two four-bladed screw-propellers, 3 ft. in diameter, at 300
revolutions per minute.
In the jurors' report, the data for estimating the power are taken as
follows: — Area of piston, 3 in., pressure in cylinder 80 lb. per
square inch, length of stroke 3 in., velocity of piston 150 ft. per
minute, 3 x 80 x 150 = 36,000 foot pounds; this makes rather more than
1-horse power (which is reckoned as 33,000 foot pounds). The weight of
the engine and boiler was only 13 lb., and is probably the lightest
steam engine that has ever been constructed. The engine, boiler, car,
and propellers together, were afterwards weighed, but without water
and fuel, and were found to be 16 lb. The council of the Aeronautical
Society agreed that this engine, as a complete working machine, met
the condition of the Society's award for "the lightest engine in
proportion to its power from whatever source the power may be
derived." The prize of £100 was accordingly allotted to Mr.
Stringfellow. ...
The exhibition, however, proved that the advocates for aerial
locomotion by mechanical means have greatly increased in number, and
their designs for accomplishing this end were as varied as they were
ingenious. But still we have no practical result by which we can
measure the progress of aeronautics in this direction; we cannot say
we have even attained the first step in actual practice. The nearest
approach that was made to this long-desired condition of things was
the demonstration that by means of vertical screws a weight of 100 lb.
might be supported by a constant force of about 90,000 foot-pounds or
three-horse power. Then we have Mr. Stringfellow's engine of one-horse
power and weighing only 13 lb., which, taken in conjunction with the
vertical screws, would appear to indicate the direction in which
mechanical flight may be realized; and this is as far as we have got —
just on the borders of possibility. But we must bear in mind the
enormous expenditure of power the system of vertical screws requires,
and the very flimsy character of an engine and boiler sufficiently
powerful to work them, and sufficiently light to allow of their
working result, if, and when attained, being made available for
transit.
It practically comes to this, that Mr. Stringfellow carried off the
£100 prize for the lightest engine in proportion to its power, but of
what real service that engine will prove to the science of aeronautics
remains still to be seen.

To understand what is going on here you need to know that John Stringfellow together with William Henson wanted to build a passenger airplane and place it into commercial service. They had drawn up plans and patented it in 1842. They tried to recruit investors. The idea of the Aerial Steam Carriage and the publicity campaign depicting the airplane in faraway places attracted considerable attention and of course mockery.
The 1848 article is describing a model airplane built as a test for the project. The tone is mocking from start to finish. They start by mocking his surname "a fine name for suspension". (Stringfellow. String. Get it?)
The part about how Stringfellow "marches through the air by a machine which sustains and propels itself through the ci[r]cumambient fluid" is deliberately over-the-top. The phrase "by a machine" suggests that the author knows it was only a model. Stringfellow is not "in a machine". He is "marching through" (conquering) the air (grandly called "the ci[r]cumambient fluid") by means of a machine which he has sent up as his proxy.
The part about exploring the Niger Valley is a riff on Stringfellows aspirations and publicity campaign. It does not mean that the author thinks Stringfellow has actual build a working full-size airplane. Again, the purple prose suggests the author is not being serious at all.
The 1868 article is describing one of two engines which Stringfellow brought to the exhibition. The smaller was mounted on a tri-plane model. The engine described in the article you quote is one Stringfellow removed from one of his old models. Its power output was estimated at 1.1 hp. The engine weighted 13 lbs without fuel or water. Stringfellow received a well-deserved prize for the technical achievement of building an engine with such a high power to mass ratio.

It's circumambient. Nevertheless, +1.

It appears that Stringfellow took the prize in 1868 (read the four articles of July 3, 10, 24 and October 9) not for the smaller engine installed on a model plane but for a larger one about which it is stated that it turned two propellers at 300 rev/min (when started, I assume for the first seconds while the pressure in the boiler was at its maximum). It is not clear whether this bigger motor was mounted on an aeroplane.

Interesting. I assumed the "car" included in the weight of the prize-winning engine was the tri-plane which ran along a wire, but I'll have to study the reports more closely.

@duofilm I think you are right. The confusion seems to stem from an account which says that Stringfellow brought to the exposition a tri-pane and a 1.1 hp engine. It is natural to assume that the 1.1 hp engine was the one mounted in the tri-pane, but then they give two sets of engine specs. I will come back and edit my answer once I have it all sorted out.

Stringfellow never built a manned machine, or even a successful model.
The Scientific American piece mistakes a model with wingspan 10 feet for a manned machine. In 1848 Stringfellow launched it from an overhead wire into a 30 yard powered glide. In his Early Flying Machines, historian Charles Gibbs-Smith notes that it "almost flew". The London Science Museum has a photo of it sat on a chair, and "Relics of Stringfellow's model of 1848: 2 wings; 1 tail; 1 hull; 1 propellor and 1 starting rail".
His 1868 exhibit at the Crystal Palace was a large steam-powered triplane model and a failure. His son F.J. Stringfellow would have no more success with a similarly powered biplane model.

Links to three primary sources are at https://en.wikipedia.org/wiki/John_Stringfellow.

I appreciate your answer but Wikipedia says: "In 1848 Stringfellow achieved the first powered flight using an unmanned 10 ft wingspan steam-powered monoplane ...The second attempt was more successful, the machine leaving a guide wire to fly freely, achieving some thirty yards of straight and level powered flight." This would mean that the model was successful because it demonstrated that level flight was possible. What I really need are contemporary evidence. I have searched online archives like: https://www.hathitrust.org but they do not say conclusively Stringfellow flew planes, even models.

@RobertWerner Wikipedia is not a reliable source (by its own admission). Claims by the likes of Parramore (who begins his book with the odd UFO sighting) are contradicted by established air historians such as Wragg and Gibbs-Smith. Note that the Gray piece cited says "straight and true" not "straight and level". Exaggerated reports were common at the time and writers who do not cite their sources cannot be believed unreservedly. There is no sensible evidence that Stringfellow's machine could sustain level flight, or even that he claimed it could. This might explain why you have found none.

The 1848 Scientific American piece is mocking in tone. It is written like a humor column, not a serious article. Note how they start by making fun of his name. The wording is also a bit over the top.


text:
Can a slow small plane, flying at a few meters above the ground, drop to the ground if the headwind abruptly stops?
Why do I ask this question? Because Wilbur Wright sent a letter to Georges Spratt (an aviation enthusiast he personally knew) saying that his plane, Flyer II, once in flight, accelerated easily to 45 mph, by itself, after reaching 30 mph. (The plane had no throttle.)
I know that once in flight, the airspeed of a plane is independent of the headwind, so it simply does not matter how fast the wind blows from in front of the apparatus. Those lulls in the wind Wilbur feared about would not have had an impact on the course of the aeroplane unless the wind suddenly dropped in intensity (this is more a theoretical case). Only then for a short time the airspeed of the plane decreases to its former airspeed minus the drop in the headwind speed, but the plane regains quickly its former airspeed.
The question is, can a low flying plane really touch the ground just because the intensity of the headwind diminishes?

We have made forty five starts with our 1904 Flyer. Unless the relative speed at starting is 27 miles in a calm and two or three miles more than that in a wind, the machine will gradually slow down till unable to fly. After the relative speed passes thirty miles the velocity accelerates till a relative speed of 45 to fifty miles is reached. We found it difficult in practice to get a speed down the track greater than 20 miles an hour, so that unless we had a wind of about 10 miles we were not sure of being able to fly for a lull in the wind would let us drop below the real flying limit. … We have now finished a starting apparatus which gives a speed at start of 27 miles an hour in a dead calm, and expect shortly to begin circling. (Wilbur Wright, “Letter to G. A. Spratt”, Dayton, Sep. 10, 1904)

Source Small plane flying at low altitude.
Update:
The topic Does a sudden drop of the velocity of the headwind affect the airspeed by lowering it? and its explanations do not answer my question. I was already aware that a sudden drop of the headwind intensity reduces for a short time the airspeed of a plane and I have already written this thing to make it clear I knew about this phenomenon.
The plane of Wilbur flew a few meters off the ground.
So, assuming Flyer II traveled at an airspeed of 30 mph against a headwind of 10 mph and suddenly the machine entered a region of perfect calm, its airspeed would have reduced to 20 mph instantly, but did the plane need to drop more than a few meters to regain its former airspeed of 30 mph?

It appears that the drop in the wind speed would have created problems only for a few seconds while the plane of Wilbur Wright was still below 30 mph. After that, from what he said in the letter, I understand that the plane accelerated quickly to 45 mph. From his explanations it appears that the headwind speed added to the ground speed of the plane all the time. Flyer II got airspeed from the headwind below 30 mph and then from a reduction of the drag as the airspeed increased!

The phenomenon described by Wright might not be related to headwind, it could have also been about aerodynamics of the Flyer. Above certain speed, the efficiency of the wings, propellers and the engine might have reached some optimal state, enabling easier flight.

One thing is sure, if nothing improved, after the plane reached an airspeed of 30 mph, Flyer II could not have reached 45 mph unless its power had increased (45 mph / 30 mph )^3 = 3.375 times. As the plane had no throttle and the engine run at constant power, tt is quite difficult to imagine a phenomenon that would have had the same effect as a more than three times increase in power.

Imagine this: the backside of the power curve

I have already wasted a lot of time, weeks, trying in Mathcad to simulate a Flyer II working on the backside of the Power Curve. The conclusion is that the plane could not have gained those 15 mph just due to the power curve profile. The gain would have been no more than 5 mph. However, no wind tunnel test have demonstrated that the drag of Flyer II decreased with the airspeed for a certain range of speeds, while in flight.

If the acceleration above 30 mph was due to headwind gust, the flyer would have very quickly decelerated back under 30mph, and further, ending the flight. This is very basic physics. Headwind can not explain what W bros experienced. They built a "faster" launcher, and expected to be able to start circling. Surely they would have not expected this, if the ability to pass 30mph was solely due to headwind.

Yes.  The theoretical concept of "moving with the airmass" essentially says that for any given constant wind or no wind, airspeed is dependent on thrust and drag and reaches a steady state.
However, in nature, especially close to the ground, obstacles such as buildings, trees and hills can make airflow anything but constant.
This is why the modern aviator adds a little airspeed when landing on windy days.  A gust or a lull can momentarily change your airspeed faster than the plane can restore its thrust/drag balance.
Wind shears are an extreme example of this.  Were it not for the wind, flying that Cessna would not be more difficult than driving a car.

Not sure that you would want to take someone from a car and throw them into a 152 and tell them "piece of cake" just because the day was windless.

No wind definitely helps, as do qualified instructors.

See also: https://code7700.com/rule_07.htm (a discussion of Vref, and the importance of adding airspeed when wind shear is anticipated).

Rule of thumb: add half of gust speed to your airspeed.

Agree with @JohnK, basic flying is not that hard, but it still does not quite compare with driving a car.

I assert that flying huge passenger jetliners is very easy.

I believe that the comments above are useless, most of them. The remark: "Were it not for the wind, flying that Cessna would not be more difficult than driving a car." was more metaphoric meaning that in calm weather it is as easy for a trained pilot (not for ordinary car drivers) to fly a Cessna as it is to drive his car.

Well, maybe some hyperbole there, but powered landings did seem easy compared with glide only with variable drag.  Learning the forward slip really helped those.

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Is there independent evidence that the Wright brothers celebrated Roosvelt's election in 1904 by a flight of over 5 minutes?
In a letter addressed to Octave Chanute, Wilbur Wright made the following statement:

Wilbur Wright, “Letter to Octave Chanute”, Dayton, November 15, 1904.
“On the 9th we went out to celebrate Roosevelt’s election by a long
flight and went around four times in 5 min. 4 sec. We unfortunately
failed to set the recording anemometer and so did not get a measure of
distance, but it was evidently a little over three miles. The trouble
in righting the machine after swinging a short circle is evidently
corrected. The machine landed without any injury and was put back on
the track for another trial, but the wind had been working more and
more to the south and we were unable to get another start.”

I guess, there should have been some witnesses, journalists, etc., present. Well then, who really saw the flight?

"we went out to celebrate" doesn't in itself imply anyone else was there -- it just means Wilbur and Orville thought about the election in connection with the date of this test.

It wasn't an important event in history when they celebrated it.

Wilbur Wright isn't a good enough witness?

The short answer is No. The independent witnesses are missing. Only Wilbur, Orville, and possible their father, saw the Nov. 9, 1904, flight.
There exists a commented collection of old documents of the period 1903-1905 (most of them from 1904), over 200 letters and articles, all quoted in full, that studies, based on primary sources, whether the Wrights really flew a plane in 1904 (they claimed 105 landings for that year).
This book is titled: "The Wrights and their impossible 1904 flights"

The 1904 plane as imagined by C. Dienstbach in his March 1905 article in German (Source: "The Wrights and their impossible 1904 flights", page 62)
Regarding the existence of the Nov. 9, 1904, flight, besides the letter sent to Octave Chanute, this is the evidence I could find, in the above mentioned work:

November 9, 1904 - An entry in Bishop Milton Wright's diary reads: “… I go on 11:00 car to Sims. At 2:00, Wilbur flew three (lacking one-fourth) miles in 5 minutes and four seconds. The distance was only limited by failure of engine.” (col. 1, p.28)
November 9, 1904 - Wilbur recorded, in one of his notebooks, a flight of 5 minutes and 4 seconds as the 82nd trial of that year. Orville also mentioned the flight in his logbook. (p. 95)
December 17, 1904 - The Dayton Press published an anniversary article, stating: "Their work and trials have been carried on quietly. They have not made any public trial, and have no intention of making any in the near future. … The longest fights yet accomplished by the machine occurred on November 9 and December 1, when the flyer made almost three miles in five minutes.” (p. 36)
December 20, 1904 - Wilbur mentions, in a letter to G. A. Spratt (a fellow aviation enthusiast), that the longest flights of 1904 occurred on November 9th, 16th, and December 1st. (col. 1, p. 18)
December 21, 1904 - Orville Wright wrote to the German journalist Carl Dienstbach saying, amongst other things,: "The two longest flights of the season were made on the 9th of November and the 1st of December. In each of these flights we made almost four complete circles and covered a distance of a little over four and one half kilometers, at a speed of about 35 miles an hour. In the flight of November 9th a weight of 50 lbs. (iron bars) were carried in addition to the weight of the operator; in the flight of December 1st, 70 lbs." The letter of Orville was published in German under the heading: “Das erste Lebensjahr der praktischen Flugmaschine”, Illustrierte Aëronautische Mitteilungen, March 1905, pp. 91-93. (p. 19)
February 3, 1904 - The Holt County Sentinel (Oregon, Missouri) published a short text that quoted the father of the two inventors: " After years of unsuccessful efforts by some of the world’s greatest scientists, it appears that the Wright Brothers, of Dayton, O., have solved the problem of the flying machine. Accounts of a successful test made by them appeared in the papers last summer, and it seems that they are making rapid strides toward perfecting their invention. We quote the following from a letter from their father, Bishop Milton Wright, of Dayton, to his niece, Mrs Frank Petree. “Wilbur, on November 9th, celebrated Roosevelt’s election by a flight of nearly three miles, in five minutes, and Orville did the same December 1st. I was there. They are improving their engine and will put the experience of 1904 into a new machine by April.” " (col. 2, p. 89)

In conclusion, the Press states that nobody saw a powered flight performed by the Wrights before December 17, 1904. The only possible witness (not really independent) of the Nov. 9th long flight could have been Bishop Milton Wright. However his diary just implies he witnessed the performance of that day. The father of the two inventors does not explicitly use the words "I saw".
If somebody else finds new evidence, in the book or from other primary sources not quoted there, I would be happy to see it.

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The stronger the headwind the faster the plane flies if it is in the reverse command regime?
Revision 3. Clarifications, as required by moderators, added. The main reason for asking the question provided.
Regarding the reverse command regime of a plane
Assuming a plane hovers (ground speed $V_{g,1}=0)$ against a headwind with a velocity $V_{w,1}$, is it possible for this plane to start moving ($V_{g,2}$ > 0) just because the wind intensifies increasing its speed from $V_{w,1}$ to $V_{w,2}$ > $V_{w,1}$?
It is known that once the plane hovers against the $V_{w,1}$ wind all its control surfaces and the power delivered to the propeller remain locked.
As a further clarification, the plane is not restricted to always stay at the same altitude. It can rise. However the power must remain unchanged.
In general, I am interested to find out if a plane can fly faster and faster as the headwind speed increases in the particular case the plane is in the reverse command regime (see definition: http://aviationglossary.com/region-of-reverse-command/ ). For the direct command regime I understand that this behavior is not possible.
Why do I ask this apparently strange question? Because it appears that a plane, in certain conditions which are not clear for me, can gain some ground speed only from the intensity of the headwind, as long as two aviation pioneers noticed this effect.
In 1904, the Wright Brothers started to test a new plane, Flyer II, somewhere near Dayton, Ohio where they managed to get permission to use a flat pasture for their experiments. The winds were light there and, in the beginning, they had no catapult to quickly accelerate their machine and throw it into the air. They simply started the engine of the airplane which began to move along a track (a runway) while a headwind of moderate intensity was blowing and finally they got into the air and flew slower if the headwind speed was lower and faster if the headwind was stronger (see letters 1 and 2).
Letter 1:
Fragment from a letter addressed by Wilbur Wright to Octave Chanute, on August 8, 1904:
"One of the Saturday flights reached 600 ft. ... We have found great difficulty in getting sufficient initial velocity to get real starts. While the new machine lifts at a speed of about 23 miles, it is only after the speed reaches 27 or 28 miles that the resistance falls below the thrust. We have found it practically impossible to reach a higher speed than about 24 miles on a track of available length, and as the winds are mostly very light, and full of lulls in which the speed falls to almost nothing, we often find the relative velocity below the limit and are unable to proceed. ... It is evident that we will have to build a starting device that will render us independent of wind."
Source: Page 52 of Octave Chanute Papers: Special Correspondence--Wright Brothers, 1904 | Library of Congress
Letter 2:
Fragment from the letter written by Wilbur Wright to Octave Chanute on August 28, 1904:
"Dayton, Ohio, August 28, 1904. Dear Mr Chanute ... ... Since the first of August we have made twenty five starts with the #2 Flyer. The longest flights were 1432 ft., 1304 ft, 1296, ft. and 1260 ft. These are about as long as we can readily make on over present grounds without circling. We find that the greatest speed over the ground is attained in the flights against the stronger breezes. We find that our speed at startup is about 29 or 30 ft per second, the last 60 ft of track being covered in from 2 to 2 1/4 seconds. The acceleration toward the end being very little. When the wind averages much below 10 ft per second it is very difficult to maintain flight, because the variations of the wind are such as to reduce the relative speed so low at times that the resistance becomes greater than the thrust of the screws. Under such circumstances the best of management will not insure a long flight, and at the best the speed accelerates very slowly. In one flight of 39 1/4 seconds the average speed over the ground was only 33 ft per second, a velocity only about 3 ft per second greater than that at startup. The wind averaged 12 ft per second. In a flight against a wind averaging 17 ft per second, the average speed over the ground was 42 ft per second, an average relative velocity of 59 ft per second and an indicated maximum velocity of 70 ft per second. We think the machine when in full flight will maintain an average relative speed of at least 45 miles an hour. This is rather more than we care for at present. Our starting apparatus is approaching completion and then we will be ready to start in calms and practice circling. Yours truly Wilbur Wright."
Source: Page 55 of Octave Chanute Papers: Special Correspondence--Wright Brothers, 1904 | Library of Congress

Assuming an airplane has a ground speed of 0, an increase in headwind would cause the airplane to move backwards over the ground. That is, if Vg1 = 0 and Vw2 > Vw1, then Vg2 < 0.

Note that the reverse command regime is unstable; you will not be able to maintain constant air speed without constantly manipulating power / control surfaces.

how can you be faster with headwind?

Gliders fly in the region of reverse command all the time, and are quite stable there thank you.

Thank you for the edit - now I understand what you ask. The Wrights were flying at the back side of the power curve where induced drag is dominant. Induced drag falls with increasing speed, and the power of the Flyer II was so limited that it had only a small speed range over which flight could be sustained. By launching into a headwind, the initial acceleration plus wind speed got the plane above the minimum sustainable speed. Without wind, the acceleration along the rail was not sufficient, and once the plane had to support its weight with its wings, drag rose above thrust.

The question of why the Wright brothers achieved higher speeds with a headwind is a mighty interesting one

@Peter Kämpf, If Thrust < Drag below 27 - 28 mph then how did Flyer II reach those speeds as long as Thrust - Drag = m*a which implies that the acceleration, a,  and speed, v, were negative. (No catapult was used.) See letter 1 from August 8, 1904: "While the new machine lifts at a speed of about 23 miles, it is only after the speed reaches 27 or 28 miles that the resistance falls below the thrust."

Simple - as long as the Flyer was on the rail, it did not create as much lift and less induced drag. Once it left the rail, acceleration practically stopped. With headwind, the rail was long enough to get it into the sustainable speed regime, without wind, it would leave the rail too slow for staying airborne. Now I hope the mods unlock this question so I can answer this properly, with graphics.

@Peter Kämpf, if moderators unlock the question, try to also write the correct plane equations in a simplified version that catches the essential, something like: (1)Thrust - Drag = m x a_horizontal and (2) Lift - Weight = m x a_vertical, covering both cases, (a) the plane sliding on the track and (2) in the air. For each situation the expressions for Thrust = ct., Drag = KD x airspeed^2, Lift = KL x airspeed^2 (these are just simplified examples) should be provided. Once I have a set of equations I can solve them in Mathcad and simulate the flight.

I upvoted, I voted for reopening - now we have to wait until more people vote for reopening. Meanwhile you might want to check a few other answers here to learn the needed equations. Or check out this.

Reminiscent of the downwind-faster-than-the-wind paradox (see for example https://en.wikipedia.org/wiki/Blackbird_(wind-powered_vehicle)).  But, totally different physics at play--

The question is not valid as asked because of a couple of factors. First, an aircraft in flight operates within a given airmass, and is unaffected by the 'wind'. Second, the 'reverse command regime' refers to an angle of attack beyond which (given constant thrust) increasing the angle of attack results in decreased net lift. In other words, the aircraft will begin to descend (or rate of descent will increase) when the stick is pulled back, i.e. the reverse of the 'commanded' climb.
If there were a wind-shear (relatively rapid increase in wind-speed), there would be a temporary increase in aircraft performance (lift and/or airspeed) due to the inherent increase in airspeed, but this will only be sustained for the duration of of the change in wind-speed. This does not appear to be what you are describing, but rapid changes in wind velocity are the only phenomena that would affect aircraft performance. In no case would airspeed be affected by a constant wind, regardless of the velocity.
Imagine an airplane flying at 100mph within an airmass that's moving at 200mph in the opposite direction; that aircraft is traveling backward (relative to the ground) at 100mph. Meanwhile, another aircraft is also flying at 100mph in the opposite direction (with the wind), resulting in a ground speed of 300mph. Both aircraft have the same airspeed; they both 'feel' the same 100mph relative wind. The movement of the airmass within which they operate is not relevant to their performance.

Because you talked about a "rapid increase in wind-speed" that can induce a "temporary increase in aircraft performance (lift and/or airspeed)", do you think it is possible that a plane flying horizontally with Vg1 against a Vw1 headwind to rise, even for a short time, its ground speed to Vg2 > Vg1 when the wind intensity suddenly gets higher changing from Vw1 to Vw2 > Vw1?

No. An increasing headwind gradient will result in a net decreasing groundspeed.

"Second, the 'reverse command regime' refers to an angle of attack beyond which (given constant thrust) increasing the angle of attack results in decreased net lift."-- this is inaccurate.  As we decrease airspeed, we get into the region of "reversed command" well before we actually see a decrease in lift coefficient, which only happens at or near the stall.  The region of reversed command is characterized by, as we slow down, a need for increased power to maintain level flight.  If we don't increase power, we find that we increase the sink rate, as we move the yoke aft and slow down.

How was the Flyer II launched into the air?
The first thing to consider is the take-off method used by the Wrights when flying on Huffman Prarie in 1904. The plane was set on a wheeled dolly which moved along a single wooden rail, the end of which was slightly elevated to give the aircraft more pitch angle and some vertical speed upon leaving the rail. This answer has some details on the rails, but centers on the catapult which was added later in 1904.
Drag components
The next is the general composition of drag in subsonic aircraft. Two main components can be distinguished, one growing with the square of airspeed and caused by friction (called zero-lift drag), and one dropping with the square of airspeed, caused by the downward acceleration of air when lift is created (called induced drag). The plot below shows them and the total drag as a green line. The drag minimum is attained at some intermediate speed. As long as the aircraft flies slower than at the speed of minimum drag, speeding up will lower the total drag.

Note that I took the liberty of adding some extra drag at the slow end of both drag curves to simulate the additional pressure drag caused by the beginning flow separation at low speed. When looking at wind tunnel data from tests on models of the 1903 Flyer (taken from Fred Culicks paper), the flow separation is apparent by the gradual decline of the lift curve slope shortly before maximum lift is reached.

I added a red line on the drag curve on the left. It shows at which lift coefficient the ratio between lift and drag is minimized, and this again confirms that the lowest drag is possible at some intermediate lift coefficient. The lift coefficient of an airplane is proportional to the inverse of the airspeed squared, so this shows again that the lowest drag is attained at some intermediate speed.
Drag increase after launch
The attitude of the airplane on the track was approximately 0°. Note that the polar above gives an angle of attack between 2° and 5° for the flight condition. This means that the aircraft produced less lift while resting on the dolly and consequently less induced drag at the same airspeed. The friction drag of the dolly should be an order of magnitude smaller than the saving in induced drag due to the reduced angle of attack during acceleration. Only when the Flyer II pitched up at the end of the track it gained the lift needed to stay it in the air.
Another effect to consider is ground effect. It lowers the induced drag component, and this effect should have helped to accelerate the Wright Flyer more while it was running along the track. Once it was airborne and had climbed some feet into the air, the speed would drop due to the climb and drag would increase due to the decreasing ground effect.
Propeller thrust over speed
The second important force is the propeller thrust, of course. In case of the Flyer II, two pusher propellers were driven by an internal combustion engine of maybe 16 HP. The power output of an IC engine is constant regardless of the speed of the aircraft and increases linearly with RPM. When driving two large, fixed-pitch propellers, the engine speed will settle at the point where the torque output equals the torque to drive the propellers. This should give the Flyer II engine a tendency to run at higher RPMs the faster the aircraft flies. However, at some point the increased aerodynamic drag of the propellers will limit this RPM increase. Around this point, the propeller thrust will change with the inverse of airspeed, since propeller thrust is power divided by speed.
The plot below is pure guesswork, but should look similar to what the Flyer II was capable of. Thrust was marginal.

Generic plot of drag and thrust over speed with fixed propellers. The plane has two trim points, one unstable point close to stall and one stable point beyond the drag minimum.
Wind speed
The last effect to consider is wind speed. When launching the Flyer II into a headwind, the airplane will have a higher airspeed at every point along the track and leave it at a higher speed than when being launched in calm wind. After launch, the aerodynamic drag increases suddenly as soon as the Flyer flies, and will increase again a little when it climbs. At these speeds, the thrust produced by the propellers will be roughly constant over airspeed - the details depend on the gearing and the engine characteristics. This means that the Flyer would be launched into the air at a point of its drag polar where drag in absolute terms was lower the more headwind was available, and the propeller thrust was not sufficient in calm air to sustain level flight. Only with the added speed possible in a headwind the Flyer could produce enough thrust to overcome the now lower drag and stay airborne.
In case of the lower headwind of 12 ft/s the plane lifted off with an airspeed of around 42 ft/s, just a bit above the slow trim point, and when it landed at the end of the field half a minute later, it had only accelerated to 48 ft/s, and the average speed over ground was only 33 ft/s. On another day with 17 ft/s headwind, the plane accelerated on the rail to maybe 47 ft/s and was well above the lower trim point at launch, so it could accelerate to the fast trim point reasonably quickly, which was maybe at 65 ft/s. Now the average speed over ground was 42 ft/s, giving the illusion that headwind made the aircraft faster. Had the flights taken longer, the speed difference between both days would had been smaller because the transient effect of the launch speed would had been smaller.

Thank you for your answer. 2) There should be other more recent and documented planes than Flyer II which, for a certain range of airspeeds, fly faster relative to the ground against stronger headwinds. If you or somebody else find such an aircraft tell me about it.

Most airplanes will fly faster over ground in a stronger headwind if you arrange for it. The behavior of the Flyer was caused by the launch method - without it the whole effect disappears. Every underpowered airplane with slowly progressing flow separation close to stall will show the same behavior in the same circumstances. You should not look for specific aircraft, but specific scenarios. A carrier launch without catapult would be such a scenario.

@ Peter Kämpf, I need the simplified equations that model Flyer II or another plane behaving in the same manner. I have tried to write these eqs. but I do not get anywhere. The plane looks to be always slowed down by the headwind.  (1) T - 1/2 * Ro * S * Vx^2 * (Cd0+Cdi) = m * ax where Cdi = k * Cl^2, (2) 1/2 * Ro * S * Vy^2 * Cl - m * g = m * ay. Help me write these equations in the correct manner. I need a simple Mathcad model that can simulate the flight against headwinds of different intensities.

Your equations look fine, and the conclusion is correct. The aircraft will fly slower over ground in a headwind. See here for an answer about the equations of motion. What you need to add is the nonlinear behavior of the lift and drag coefficients at higher angles of attack.

I have already added that nonlinear dependency either as Cd = Cd0 +  k * Cl^2 or extracting Cd=Cd(Cl) from the diagram: "Lift and Drag curves for a typical airfoil" (see: https://en.wikipedia.org/wiki/Lift-induced_drag ). The non-linearity of the functions Cd = Cd(alfa) and Cl = Cl(alfa) does not seem to speed up the plane as the headwind intensifies.

@RobertWerner: Do I get the impression that you expect the aircraft to magically speed up in a headwind? This will not happen. You need boundary conditions which place the aircraft at a higher forward speed in a headwind, like a limited take-off run. All by itself it will fly with the same speed relative to the air, and slower relative to the ground when the wind blows.

@ Peter Kämpf, What I expect in general is to fly faster against stronger headwinds (for low airspeeds) because this is what the Wrights said: "In one flight of 39 1/4 seconds the average speed over the ground was only 33 ft per second, a velocity only about 3 ft per second greater than that at startup. The wind averaged 12 ft per second. In a flight against a wind averaging 17 ft per second, the average speed over the ground was 42 ft per second, an average relative velocity of 59 ft per second". A wind-speed increase of 5 ft/s made the plane 9 ft/s faster, for time intervals ~ 39 sec!

@RobertWerner: I made an edit to the answer. If you don't get it now, I will give up.

Let us continue this discussion in chat.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
What engine of the period 1855-1865 would have lifted one of Wright brothers' aeroplanes off the ground?
On December 13, 1905, the Wright brothers sent a letter to Georges Besançon, the editor of L’Aérophile, a leading French aeronautical journal. L'Auto, a newspaper of Paris, published a part of the text (see the French article below - it can be read with Google Translator).
The last paragraph, which I already rendered in English, contains a claim, of the two Daytonians, saying that their 1905 apparatus was so well designed that even engines built as far back in the past as 1855 could make it fly:

Ordinary landings do not damage the apparatus at all, and flight after
flight are performed without any repairs. The success results from the
high scientific efficiency (sic) of the airplane and propellers and
especially from the recent improved methods of balancing and steering.
It has often been said during the nineteenth century that it was above
all the lack of sufficiently light engines that prevented man from
conquering the air. This opinion is strongly contradicted at ordinary
bird speed, a well-studied airplane can currently support a weight of
30 kilograms per horse, which gives ample room for engines built even
fifty years ago ...

Question: Can anybody offer an example of such an old motor, made say between 1855 and 1865?
The full article in French:
1905-12-29, “Nouvelle lettre des frères Wright”, L’Auto, Paris, December 29, 1905, col. 5-6, p. 3.

Nouvelle lettre des frères Wright
Les célèbres inventeurs donnent de nouveaux détails
Les méthodes de mesure. — Vitesse par rapport à l’air et parcours
mesuré au sol. Avec un aéroplane bien combiné et bien manœuvré les
résultats actuels auraient pu être obtenus depuis cinquante ans?
Le débat engagé autour des affirmations des frères Wright à la suite
de l’article de l’Auto du 30 novembre n’est sans doute pas près de se
clore. L’enquête de notre collaborateur Robert Coquelle, faite sur les
lieux mêmes, nous a révéle d’intéressents détails. Nous sommes heureux
d’apporter encore aujourd’hui de nouveaux éléments, d’appréciation en
mettant sous les yeux de nos lecteurs les principaux passages d’une
nouvelle lettre en date du 13 décembre, adressée par les frères Wright
à l’excellente revue d’aéronautique L’Aérophile, qui leur avait
demandé des renseignements complémentaires sur leurs expériences.
Cette fois encore nous sommes en présence des déclarations des
intéressés eux-mêmes, et certaines, d’entre elles seront de nature à
raviver le débat:
Dayton, 13 décembre 1905.
Monsieur le Directeur, ...
Voici les nouveaux détails que nous croyons devoir vous donner:
Le terrain où ont en lieu nos expériences les plus récentes est une
prairie plane ayant à peu près huit dixièmes de kilomètre de longueur
et quatre dixièmes de kilomètre de largeur, mais d’une forme si
irrégulière que les cercles décrits avaient à peu près 1 kil. 500
mètres.
La longueur des vois était mesuré avec un anémomètre Richard monté sur
l’appareil, de façon à commencer à enregistrer quand l’aéroplane
partait et à s’arrêter quand le moteur stoppait. Comme le moteur était
arrêté un instant avant l’atterrissage, les vols se trouvaient en
réalité légèrement plus longs que la distance enregistrée.
Lorsque les vols se faisaient en ligne droite par temps calme, les
indications de l’anémomètre correspondaient très bien avec le parcours
réel mesuré sur le terrain. Quand, au contraire, les vols étaient
exécutés en cercle autour du champ, il n’était pas pratique de mesurer
exactement le trajet sur le sol. Les distances sont celles
enregistrées par l’anémomètre. Le vol de 39 kilomètres comportait 29
circuits sept dixièmes autour de la prairie. Le temps était pris par
trois chronographes dont un fixe à l’anémomètre.
La vitesse en l’air, à peu près la même pour toutes les vols, était
d’environ 1 kilomètre par minute. La vitesse par rapport au sol a
varié naturellement, en des parties différentes de la course, selon la
fonce et la direction du vent. Dans les vols des 3 et 4 octobre 1905,
l’aeroplane fut constamment maintenu à 25 mètres au-dessus du sol.
Mais dans les expériences antérieures, nous avons parcouru milles sur
milles sans monter une seule fois à plus de 3 ou 4 mètres de hauteur.
Quand nous volions bas la vitesse semblait beaucoup plus grande que
lorsque nous tenions moins près de terre.
Pour l’instant, nous, préférons ne pas donner plus de détails sur
notre machine. Notons seulement que la légèreté n’a pas été cherchée.
L’appareil ne comporte aucun dispositif aérostatique, ni quoi que se
soit de plus léger que l’air. Les organes du moteur, tel que
cylindres, pistons, bielles, etc., etc., sont du poids ordinairement
usité en construction automobile. Les plans porteurs et le bâti de
l’appareil sont établis beaucoup plus lourd qu’on n’a l’habitude de le
faire dans les machines volantes.
Les atterrissages ordinaires n’abîment pas du tout l’appareil, et vols
après vols sont exécute sans aucune réparation. Le succès résulte de
la haute efficacité scientifique (sic) de l’aéroplane et des hélices
et spécialement des méthodes perfectionnées récentes de balancement et
de direction. On a souvent dit, pendant le dix-neuvième siècle que
c’était surtout le manque de moteurs suffisamment légers qui empêchait
l’homme de conquérir de l’air. Cette opinion est tout à fait
controuvée a la vitesse ordinaire de l’oiseau, un aeroplane bien
étudier peut actuellement soutenir un poids de 30 kilos par cheval, ce
qui donne amplement de la marge pour le moteurs construits même il y
cinquante ans …
Signé: Wilbur et Orville WRIGHT.

Why is it OK to Ask that with no relevant research… ie, here's a wing with X-much lift, so it needs Y-power, provided by a propellor driven by a gear-set powered by the engine you're asking about?

related-- new chat room -- https://chat.stackexchange.com/rooms/123457/were-the-wright-brothers-claims-wildly-exaggerated-especially-re-1903-1904

First, I would like to mention a free book, that I skimmed a few days ago, which reached the conclusion that the Wrights committed one of the greatest technical frauds of the twentieth century. The text concentrates on the 105 flights of 1904. The work is based only on primary sources, mainly documents of the period 1903-1905, in majority letters of the two brothers and the answers received by them, plus newspaper articles (all quoted in full).
After reading the letters and articles you start to ask yourself how is it possible that so many authors credit Wilbur and Orville Wright with building the first heavier-than-air man carrying plane that ever flew when, in fact, the two inventors just tried to fool the newspapers (especially those of Dayton), Octave Chanute (a personality of the aeronautic world of the time), Georges Spratt (a fellow aviation enthusiast), Carl Diesentbach (the New York correspondent of the German journal "Illustrierte Aeronautische Mitteilungen") and both the US War Department and British War Office, by pretending they had performed no less than 105 flights in 1904 and, in many instances, describing aerial trips that are physically impossible, like the ones of August 13, 1904, when the plane, Flyer II, got energy from the headwind, which accelerated the apparatus.
"The Press", the only newspaper that, on May 26, 1904, furnished a list of witnesses (friends of the Wright family and an unnamed reporter) who saw the alleged flight of the same day, later in the year, on December 17, 1904, acknowledged that nobody had ever seen the two inventors flying powered planes.
The Wrights and their impossible 1904 flights

Now, to give an answer to the question of whether about 50 years before 1905 there existed engines capable of powering a plane, I would say that (see the clipping from the Scientific American of March 13, 1869) John Stringfellow won (after June 1868) a prize of 100 pounds for a steam motor that developed an estimated max power of 1.14 hp and weighted 5.89 kg but without water.
The Wright brothers might have heard about this engine, form Octave Chanute, for example, and scaled it up 20 times reaching the conclusion that a 22.8 hp motor with a mass of 117.9 kg was possible in 1868. However, this is pure math.

Source: Scientific American. / New Series, Volume 20, Issue 11, p. 169; Mar 13, 1869, New York
(As a note: An earlier article which appeared in the September 23, 1848, issue of the Sci. Am. and mentioned some experiments performed by a certain Mr. Stringfellow, is vague. The text contains no clear description of what the inventor did.)

Interesting to read that in 1868 the lack of proper materials was cited as the main reason preventing the construction of flying machines. Wooden gliders show that even with the technology of the late Middle Ages gliding flight would had been possible. What was really missing was a lightweight, powerful and reliable engine. +1

Related-- https://aviation.stackexchange.com/questions/82108/is-there-any-clear-picture-or-drawing-of-a-wright-brothers-plane-published-be , https://aviation.stackexchange.com/a/81263/34686

@RobertWerner -- chat room now created -- https://chat.stackexchange.com/rooms/123457/were-the-wright-brothers-claims-wildly-exaggerated-especially-re-1903-1904

I temporarily accepted this answer because it provides: (1) the technical characteristics of a plane engine built before 1870 and (2) in that book "The Wrights and their impossible 1904 flights" (see: http://wright1903dec17.altervista.org/The-Wrights-and-their-impossible-1904-flights-Book-by-Bogdan-Lazar.pdf) at pages 31-33, the technical characteristics of Flyer I and II (also III), including information about their motors, as stated by the Wright brothers themselves. However, I might change my mind and select another answer.

This Wright hoax idea is barking mad conspiracy stuff. I have read much contemporary UK source material, including accounts by Col. Capper, Superintendent at Farnborough, who visited the Wrights with his wife and became personal friends. They discussed aeronautics on level terms. The Wrights clearly knew what they were doing and this imagined hoax would have been more work than the effort put in to making it actually happen. The Flyer III was way ahead of the world when it appeared, and that did not evolve out of Machiavellian timewasting.

@GuyInchbald , Incidentally, in the book "The Wrights and their impossible 1904 flights", ( see the chapter: "Wright brothers - British War Office negotiations, Sep. 16, 1904 - Feb. 8, 1906." p. 64, you can read in full the exchange of letters between the Wrights and Col. Capper, the British War Office, Col. Foster. The two inventors refused to show any plane and the WO in London was unwilling to start negotiations with them before seeing something. The Wrights wanted to sign a contract with the gov. of GB without showing anything also they claimed things that nobody did before!!

@duofilm Other contemporary correspondence in various UK archives shows that Col. Capper's personal influence and knowledge overcame this obstacle. The War Office insisted that the planes be demonstrated to them and flying lessons given to a few soldiers, before they paid up. The Wrights agreed. The deal only fell through because the Wrights demanded a thousand dollars a plane and the War Office were not prepared to pay that; they argued that Capper's in-house pioneer, Lt. J.W. Dunne, could make a better plane for a lot less. You have been fooled by a clever cherry-picker.

The actual page number of the 1869 Scientific American article is 169, not 69:
https://babel.hathitrust.org/cgi/pt?id=pst.000062999229&view=1up&seq=179

@GuyInchbald , I do not believe I was fooled because the letters, in that chapter I mentioned, have each a reference, with a clickable link. Therefore, I went directly to the original archive at the Library of Congress and read all letters from there. The negotiation between the Wrights and the WO fell apart again on Dec. 3, 1906, and were restarted for the 3rd time by the Wrights on Apr. 10, 1908, too late because, in France, Farman had already flown 2 km in front of official witnesses and planes were available for sale. (As a note, the Wrights did not show any plane before Aug. 8, 1908.)

@David42 , I have made the correction and added your link which was better than mine. As a remark, when you quote pages from articles in hathitrust.org, do not give the address that starts with "babel" but the one which begins with "hdl" that can be found below "Link to this page" (ex.: https://hdl.handle.net/2027/pst.000062999229?urlappend=%3Bseq=179). This is the permanent address, the other one can change in time.

@duofilm You must have missed (to take one example) the letter they wrote to the War Office on Oct 19, 1905, conceding an increase in the trial flights before acceptance (and hence payment). Even then, as I said the Wright correspondence does not give the whole story. The War Office, Col. Capper and others also corresponded with each other. You need to check those records too. Gollin gives a fairly comprehensive account in No Longer an Island (Heinemann 1984).

@GuyInchbald , The US War Department also stopped the negotiation with the Wrights, on Oct. 27, 1905, demanding first a horizontal flight before taking any further action. When the two inventors had reopened the negotiations, on Oct. 9, 1905, they did not even mention the series of spectacular long public flights (according to them) that had ended on Oct. 5. What they were afraid of? They wanted to sign a contract with the US government without showing any evidence they had built and flown a plane, an apparatus that nobody succeeded to fly before!

@duofilm Keep your crazy-logic speculation to yourself. I prefer documented fact. But you might like to consider that most contracts are for the supply of deliverables and not for proof of pre-existence. Over and out.

@GuyInchbald , If you want more documented facts then read this article in the Wilmington Messenger (North Carolina, May 26, 1904, col. 1, p. 6 - see: https://aviation.stackexchange.com/questions/82108/is-there-any-clear-picture-or-drawing-of-a-wright-brothers-plane-published-be ). A man that worked for the Wrights said that the two brothers had not finished the December 1903 plane and he was waiting for them to continue their work. This statement corroborates well the 1951 declaration of A. Drinkwater who said the first flight of the Wrights took place on May 6, 1908, not on Dec. 17, 1903.

50 years before, in 1855, not even the Lenoir engine, a two-stroke combustion engine which ran on natural gas (saving Lenoir from inventing the carburettor after having invented the spark plug already) had been invented yet.
This only leaves steam or compressed air engines - ignition engines needed inventions which only occurred in (induction coil by Rühmkorff) or after 1855. The lightest ones would be fireless and rely on a reservoir of high pressure steam or air, allowing only a very short operation. However, even the earliest fireless locomotives were only invented after 1855.
Carbonic acid engines were indeed used to power very early airplane designs and were initially developed in the 1820s, so they would had been technically feasible. But nobody tried them for aviation before the 1890s, probably because the first such machines were unfavorably compared to a ticking time bomb.
I think the Wright brothers claim is preposterous and reeks of arrogance. No wonder they were titled "the lying brothers" at this time.

There may be a cultural aspect here if you are assigning the year1855 is a hard truth-or-lie value.  Nothwithstanding whether or not one of Lenoir's engines from the 1860s was capable of making the power to weight, Wright's mention of "50 years ago" wouldn't be taken as a literally, exactly at least 50 years ago by American or Canadian ears.  If you say you were were doing some activity 50 years ago, I will just assume some time in the early 70s.  I wouldn't accuse you of lying if I found out the actual year was 1975.  The Wright statement of 50 years I take as "mid 1800s", not exactly 1855.

@JohnK Thank you for the hint, I should rephrase the answer. However, it took at least until the last decade of the 1800s for power to weight ratio to become feasible for flight. Even Hiram Maxim preferred a steam engine as late as 1894. Lenoir's engine of 1863 could only produce 1,5 HP from a displacement of 2.5 liters.

Agreed.  He probably threw that line in without really researching it, or was doing what is known in sales as "puffery" or exaggerating for effect (the letter could be thought of as a marketing document).  The Wrights' own motor was pretty interesting, considering how crudely it was fashioned.  The crank started out as a steel slab with the crank profile roughed out with a drill press!  The EAA built an exact copy of their motor and runs it at Oshkosh.  Sounds like a 4 cyl farm tractor.

I don't understand the hostile tone of this answer. How is it relevant that from 1903 to the spectacular public demonstrations of 1908 reports of the Wright brothers' growing success were widely disbelieved? This answer is also weak because it ignores the quantified claim made in the letter: that the Wright machine required only one horsepower per 30 kg. I think you need to identify the first engine which would have worked in their machine. If it was available decades earlier to the previous generation of aviation pioneers, then their claim is true in substance, though perhaps not in detail.

The aviation enthusiasts to whom this letter was address in 1905 would have understood the Wright brothers to be referring primarily to special light-weigh steam engines specifically designed for use in aircraft. Enthusiasts had been building such engines since at least the 1840’s and by the 1870's you could have one built for you if you could afford it.
The statement made by the Wright brothers has two parts: 1) It is a mistake to conclude that 19th-century aero-engines had insufficient power for flight simply because the flying machines in which they were mounted failed to fly, and 2) suitable engines existed 50 years ago. The first statement is almost certainly true. The second statement is true only with the major qualification that the engines actually build before the 1870's seem to have been small-scale prototypes.
In 1905 when the Wright brothers wrote this letter the only working powered airplanes (other than their own) are models too small to carry a pilot. As far as the Wright brothers know nobody has been able to get a man-carrying airplane more than a meter into the air, keep it there for more than a few seconds, and travel more than 100 meters along the ground.
We now now that there are at least six principal reasons why 19th century airplanes did not work: 1) The wings had a poor lift to drag ratio, 2) The propeller blades did not have the shape they would need to provide good thrust for the input power, 3) the airplanes lacked three-axis control, 4) the controls they did have were difficult to operate, 5) the operators did not know how to fly an airplane, and 6) the steam engines were not powerful enough to overcome problems one and two.
The Wright brothers are reporting that they now have an airplane which actually flies. They have achieved this by attacking problems one through five. If you solve all of them, you do not need to solve problem six.
Their core claim about airplane engines is expressed in numbers. They say that with their design improvements an airplane can fly with an engine which produces only one horsepower for every 30 kg of gross vehicle weight. This is an approximation of what they actually achieved on December 17, 1903 at Kitty Hawk with an airplane which weighted 338 kg and a 12 hp engine (28 kg/hp).
This claim is also in line with what other researchers had already discovered. The Wright brothers had read Octave Chanute’s 1894 book Progress in Flying Machines in which he reports (p. 73) tests of airplane wings (not entire airplanes). Professor Langley found that a wing could lift 200 lbs (90 kg) per horsepower while Mr. Maxim’s tests yielded a figure of 133 lbs (60kg).

The 1903 Wright engine as seen in 1916 after restoration
The homemade 12 hp engine used by the Wright brothers weighed 170 lbs dry. With fluids it weighted about 200 lbs. In 1903 it produced between 12 hp continuously and 16 hp peak (7.5 and 4.6 kg/hp respectively). This is very modest performance for a gasoline engine. For comparison the Clerget 9B used in the Sopwith Camel in 1917 weighted 173 kg (dry) and produced 130 hp which is 1.33 kg/hp (slightly worse with fluids of course).
While it is difficult to find reliable and detailed information about the performance of 19th century steam aero-engines, it is clear that a number of them had power to mass ratios equal to or better than that of the Wright engine.

1843: William Hensen and John Stringfellow obtained a British patent for the concept of an "Aerial Steam Carriage". This was to be a passenger airliner with a 150 foot wingspan driven by a 50 hp light-weight steam engine. They sought investors and began experiments with a model with a 20-foot wingspan and a working light-weight steam engine. They conducted tests between 1843 and 1847. Though the engine worked, making the even a large-scale model strong and stiff enough to fly outdoors proved beyond their ability.
Some notes from a bench test of the engine have been preserved:

June, 27th, 1845, water 50 ozs., spirit 10 ozs., lamp lit 8.45, gauge moves 8.46, engine started 8.48 (100 lb. pressure), engine stopped 8.57, worked 9 minutes, 2,288 revolutions, average 254 per minute. No priming, 40 ozs. water consumed, propulsion (thrust of propellers), 5 lbs. 4 1/2 ozs. at commencement, steady 4 lbs. 1/2 oz., 57 revolutions to 1 oz. of water, steam cut off one-third from beginning. The diameter of cylinder of engine was one-and-a-half inch, length of stroke three inches.

Note that it took three minutes to get up steam and the engine ran for nine minutes. If we estimate the average pressure in the cylinders at 50% of the boiler pressure, this engine produced about 1/6 hp.

Photograph of Stringfellow's 1848 model airplane

Photograph of one of the numerous surviving Stringfellow aero-engines
1848: John Stringfellow builds a smaller model with a 10-foot wingspan and a new engine. According to Chanute, Stringfellow tested it indoors in a room less than 66 yards long. It ran one third of the length of the room along a guide wire. After leaving the wire it would continue to fly to the end of the room. If would frequently rise after leaving the wire at a rate as high as one in seven. The weight of the entire model including engine, water, and fuel was less than 6 ½ lbs.
In 1995 a reproduction of Stringfellow's 1848 model was build for the BBC2 program Local Heroes. This model was tested in the same mill Stringfellow had used. A published advertisement for the program implies that the model flew. I would like to know more about this program.

According to the Smithsonian this is the Stringfellow engine which won a Royal Aeronautical Society prize for best power to mass ratio in 1868. It is unclear when the engine was built. Stringfellow wrote he had removed
it from an unspecified "old model" to take it to the exhibition.
1868: The Royal Aeronautical Society held a show in the Crystal Palace in London. Due to his reputation, John Stringfellow was invited to exhibit one of his models. He got them out of storage but decided none was in sufficiently good condition and so built a new tri-plane model with a 1/3 hp steam engines. During the exhibition it ran along a wire stretched across the exhibition hall. Free flight was not allowed due to the fire risk, but the machine seemed to lift the wire.
Stringfellow also exhibited a steam engine removed from one of his old models. The cylinder was two inches in diameter, the stroke length three inches. The working pressure 100 psi. It drove two four-blade propellers, three feet in diameter, at 300 rpm. As reported in Is a Flying Machine a Mechanical Possibility? (Scientific American, March 13, 1869, volume 20, Number 11, p. 169) the power was estimated as follows:

Area of piston, 3 inches; pressure in cylinder, 80 lbs. per square inch; length of stroke, 3 inches; velocity of piston, 150 feet per minute; 8 x 80 x 150 = 36,000 foot-pounds. This makes rather more than one-horse power (which is reckoned at 33,000 foot-pounds). The weight of the engine and boiler was only 13 lbs., and it is probably the lightest stream engine that has ever been constructed.

(This calculation seems to imply that the cylinder was double-acting. It also estimates that the average pressure in the cylinder was 80% of the boiler pressure which seems generous.)
If this engine used twice as much water and fuel as the 1845 engine (which was filled with 50 oz of water and 10 oz of fuel), that would add about 1.6 kg to the weight for a total of about 7.5 kg. That works out to 6.8 kg/hp, about the same as the Wright engine, albeit at a smaller size. Mr. Stringfellow was awarded a prize for the best power to weight ratio yet achieved in a steam engine.
1874: Félix and Louis du Temple tested a monoplane powered by a steam engine of their own design. The engine was equipped with a boiler in which small pipes were tightly packed into a lightweight firebox. According to Chanute (Progress in Flying Machines, 1894, pp 90-92) the machine, which was intended to carry a man, had a wingspan of 40 feet and weighted about 160 lbs. According to Sobolyev (История самолетов мира, 2001, p. 27) the engine weighted 59 kg. If it developed the 6 hp some sources suggest, then that is 9.83 kg/hp, worse than the engine in the Wright Flyer.

Plans for Mozhaychy's 1884 Monoplane

Drawing of the 10 hp engine which Messrs. Ahrbecker, Son & Hamkens, of Stamford Street, S.E. made for Captain Mozhaysky
In 1884 Russian naval officer Alexander Mozhaycky tested a steam-powered monoplane with two stream engines imported from England. According to Sobolyev (История самолетов мира, 2001, p 29) one engine produced 10 hp, the other 20 hp. He gives the combined mass to power ratio of the entire propulsion system including both engines, boiler, condenser, and separator as 5.5 kg/hp which is better than the performance of the Wright engine as measured in 1903. Sobolyev (p 30) quotes a report (Военная энциклопедия. Т16, Спб., 1916. С. 377) which reads “The apparatus rose from the ground, but being unstable it tipped onto its side and broke a wing”.
The engines were described in the Scientific American Supplement for the years 1881 and 1882 as follows:

The larger of these engines has cylinders 3¾ in. and 7½ in. in diameter and 5 in. stroke, and when making 300 revolutions per minute it develops 20 actual horse power, while its weight is but 105 lbs. The smaller engine--the one illustrated--has cylinders 2½ in. and 5 in. in diameter, and 3½ in. stroke, and weighs 63 lbs., while when making 450 revolutions it develops 10 actual horse power.

The two engines are identical in design, and are constructed of forged steel with the exception of the bearings, connecting-rods, crossheads, slide valves and pumps, which are of phosphor-bronze. The cylinders, with the steam passages, etc., are shaped out of the solid. The standards, as will be seen, are of very light T steel, the crankshafts and pins are hollow, as are also the crosshead bolts and piston rods. The small engine drives a single-acting air pump of the ordinary type by a crank, not shown in the drawing. The condenser is formed of a series of hollow gratings.

Steam is supplied to the two engines by one boiler of the Herreshoff steam generator type, with certain modifications, introduced by the designers, to insure the utmost certainty in working. It is of steel, the outside dimensions being 22 in. in diameter, 25 in. high, and weighs 142 lb. The fuel used is petroleum, and the working pressure 190 lb. per square inch.

1890: Clement Ader tested a steam-powered monoplane with bat-like wings. It was equipped with a 20 hp engine weighing 51 kg (2.55 kg/hp). With a gross weight of 330 kg the machine weighed the same as the 1903 Wright Flyer, but had 67% more engine power. Ader’s machine rose about 25 cm off the ground and flew for about 50 meters.

Sir Henry Maxim's test rig which was damaged on July 31, 1894 when the captive flying machine lifted and tore itself off of the track before the dual 180 hp steam engines could be stopped

Sir Henry Maxim holds one of his 180 hp steam aero-engines

1894: Sir Henry Maxim operated a test rig for experiments with various wing configurations. In the April 1910 issue of the Journal of the Western Society of Engineers Octave Chanute described the experiments as follows:

Mr. Maxim built an enormous apparatus, weighting 8,000 pounds and spreading 4,000 feet of surface, moved by a steam engine of 360 horsepower. That machine was run upon a track of 9 feet gauge a good many times, and on one occasion it undertook a vagabond flight on its own account; its equilibrium was bad, however, and the steam was shut off; the machine alighted somewhat broken.

According to Sobolyev (История самолетов мира, 2001, p. 34) the engines, boiler, and condensers together weighted about a tonne for a mass to power ration of 3.1 kg/hp. At 8,000 lbs gross weight and 360 horsepower the Maxim test rig had one horsepower for every 10 kg of gross weight. That is nearly three times as much engine power per unit of vehicle mass as the 1903 Wright Flyer had.
Maxim, in his thesis Natural and Artificial Flight (Excerpted in The Aeronautical Annual, 1896, published as Artificial and Natural Flight in 1908) describes his experiments in detail and concludes:

My experiments have certainly demonstrated that a steam engine and boiler may be made which will generate a horsepower for every six pounds of weight, and that the whole motor, including the gas generator, the water supply, the condenser, and the pumps may be all made to come inside of 11 lbs. to the horse-power. They also show that well made screw propellers working in the air are fairly efficient, and that they obtain a sufficient grip upon the air to drive the machine forward at a high velocity; that very large aeroplanes, if well made and placed at a proper angle, will lift as much as 2 and a half lbs. per square foot at a velocity not greater than 40 miles an hour; also that it is possible for a machine to be made so light and at the same time so powerful that it will lift not only its own weight but a considerable amount besides, with no other energy except that derived from its own engines. Therefore there can be no question but what a flying machine is now possible without the aid of a balloon in any form.

So after experiments this respected aviation pioneer concluded that it was perfectly possible to build aero-engines weighing less than 5 kg/hp and that a steam-powered airplane was definitely possible.
1897: Samuel Pierpont Langley, secretary of the Smithsonian, achieved sustained powered flight with two large models equipped with steam engines which ran for up to two minutes. Interestingly in 1889 Langley had bought at least one Stringfellow engine from the inventor's son and sent it off for study.
In conclusion, when the Wright brothers wrote this letter they could allude to a well-known history of steam aviation engines stretching back more than 50 years. The steam aero-engines actually installed in actual man-carrying airplanes build and tested in the last quarter of the 19th century likely had a power to mass ratio comparable to that of the homemade gasoline engine used by the Wright brothers in their 1903 Flyer. While one can find fault with the "50 years ago" part of the statement, the overall statement that 19th century aero-engines were sufficient for sustained flight is sound.

Are there flying models of Stringfellow's 1848 model plane? Had the 16 lb engine+boiler of John Stringfellow really generated 1.1 hp, continuous power, it would have become, then in 1868, an extremely successful motor for powering tools (like a lathe) in small workshops, for powering small river boats, steam cars, draisines, even bicycles. In reality, Stringfellow's motor worked in pulses of a few seconds, below 10 s, followed by at least a 4-minute pause necessary for rebuilding the steam pressure. If you do the math you will see that it needs about 1.5 L of steam at 5 atm per second.

I was unable to find information about the output power of the 1848 engine. The 1.1 hp figure is for his 1868 engine and comes from the Scientific American. I did not get into the question of runtime because I don't think they are talking about practical airplanes here. They are talking about what it takes to make an airplane stay in the air for more than ten seconds and fly more than 300 feet. I have chosen to interpret their statement charitably. As readers of Chanute they would know that a kind of engine which could do that had been invented more than 50 years ago.

@RobertWerner Exactly. Lilienthal earned the money for his gliding experiments by building small and efficient steam engines (Schlangenrohrkessel-Dampfmaschine) which he initially developed to power flying machines. Those machines were very successful powering small factories or larger workshops but Lilienthal considered steam engines as unsuitable for flight, relying later on carbonic acid engines.

Using the empty weight of a steam machine for power to weight comparisons with internal combustion machines is totally misleading, bordering on manipulation.

@PeterKämpf I agree and have tried to avoid doing so. In some cases it is unclear whether figures quoted in sources include water and fuel. Would you like to suggest any specific corrections?

I would welcome any help to expand and improve this answer. In particular, I would be curious to know what was the first aero-engine actually built which might plausibly work in the 1903 Flyer. I am intrigued by Sobolyev's statement that Mozhaycky bought his engines.

@David42 , Regarding Clement Ader, I have found an article: "L'oiseau de M. Ader", Le Temps, Paris, July 9, 1891, col. 3-4, p. 2 ( see: https://gallica.bnf.fr/ark:/12148/bpt6k2329887/f2.item ) The author of the text says: "Installé dans un appareil affectant la forme d'un énorme oiseau, il [Ader] parvenait à s'élever dans l'espace et à parcourir une faible distance: une centaine de mètres, disent les témoins incrédules; 400 mètres disent les enthousiastes.". However, Ader himself in the long interview that follows the introduction says that he experimented. He does not claim he flew his plane.

Translation of the French text quoted in my previous comment: "Installed in an apparatus having the form of an enormous bird, he [Ader] managed to rise in space and to cover a small distance: a hundred meters, say the incredulous witnesses; 400 meters say the enthusiasts." This looks like publicity. Had he flown, Ader would have mentioned this during the interview.

@duofilm It is generally accepted by aviation historians that Ader made a "powered hop" in the Éole of 50 meters 20 to 25 cm above the ground on Oct. 9, 1890. While this was an interesting experimental result and even a world first, it did not make the Éole a successful flying machine. At the time of the interview he may have considered these results disappointing. If you have any suggestions for improving the section on the Éole and the capabilities of its engines, please let me know. What we want to know is whether his engines could have flown if mounted on a better airplane.

I have rewritten the introduction and conclusion to make it clearer that which part of the Wright statement I consider well-founded and which part is more dubious. I also plan to add more information about  Captain Mojaisky's engines and where and when he got them.

@David42 , "It is generally accepted" if we believe texts like this: "Ce problème, s'il faut en croire les feuilles publiques, un Français, M. Ader, l'aurait résolu. Au moyen de combinaisons ingénieuses, qui restent encore un secret, il serait arrivé à se soutenir dans l'air et à s'y diriger. On raconte que dans le parc d'un riche banquier des environs de Paris il s'est élevé à 20 mètres au-dessus du sol et a parcouru un espace de 400 mètres, à la stupéfaction du public très restreint admis à ces expériences." - Oct. 2, 1891 - (https://gallica.bnf.fr/ark:/12148/bpt6k55853675/f13.image.r=ader)

@PeterKämpf I think you need to qualify "Using the empty weight of a steam machine for power to weight comparisons with internal combustion machines is totally misleading, bordering on manipulation." Both have hidden loads; water and fuel on the one hand, but also lubricant, fuel and possibly coolant on the other. An efficient flash steamer such as Maxim's can have excellent power-to-weight for short flights.

I came across a chart a while ago, showing the development of power-to-weight in aero engines from antiquity to the Wrights. Drawn up by a respected figure of the day, it bears out both the Wrights' claim and this answer very nicely. If I can find it again I'll post it here.

@David42 You ask what engine might have plausibly been used. Bear in mind that propeller efficiency is a vital, and often forgotten, ingredient. The Wright engine was low-powered by any standards, but they developed more efficient propellers than the old bent-sheet-on-a-stick type. Whitehead reputedly funded his controversial flying cars from making aero engines. Coupling one of those to a Wright propeller might have been interesting.

@duofilm Ader's claims sound like a good subject for a separate question. I don't think we can address the issue properly here in a question about 19th century aero-engines. Since you know French and can read the primary sources, your participation would be valuable.  It would be great if someone could find Ader's October 12, 1890 letter to Nadar in which he describes the October 9 experiment or the written statement made by one of his assistants. Ader's letter is supposedly preserved in the National Library in Paris. If you create a new question, please put a link in the comments here.

@GuyInchbald I agree. The Wright brothers mention increased propeller efficiency explicitly in their statement quoted in the question. I also address it above in paragraph four. It strengthens their statement greatly. My call for the identification of plausible candidate engines was posted as a criticism of another answer which simply lists engines and engine technologies which were unsuitable or unavailable. I spent almost a week attacking the problem from the other end, by asking what 19th century aviators were actually using. This proved far more fruitful and the answer above is the result.

@David42 , Apparently, a user read your mind and has already asked a question about Ader's flight of Oct. 9, 1890 (see: https://aviation.stackexchange.com/questions/86917/is-there-strong-evidence-that-clement-ader-flew-a-plane-on-oct-9-1890-or-at-an ). Based on the letter you mentioned and this book: "Ader, Clément, "La première étape de l'aviation militaire en France", Paris, J. Bosc et Cie, 1907" (http://cnum.cnam.fr/CGI/redir.cgi?A890 ) you could answer the question. However, what Ader claimed in the book might not be true.


text:
Regarding the 1902 Wright glider. Why is the airspeed, Va, calculated adding the ground speed, Vg, and wind speed, Vw?
Regarding the 1902 Wright glider. Why is the airspeed, Va, calculated adding the ground speed, Vg, and wind speed, Vw?
In August 1903, Octave Chanute published in L'Aerophile a table (see attached) showing the measured quantities:
(1) distance traveled along the ground (col. 2),
(2) flight time (col. 3),
(3) wind speed (col. 5),
(4) glide angle (col. 7),
corresponding to a few flights performed on Oct. 8, 1902. From these parameters and the total mass of the machine and pilot, O. Chanute calculated that the 1902 glider lifted about 62 kg/hp (see the last column).
It is not quite clear for me why Va = Vg + Vw (see col. 6). The airspeed should be constant, independent of the headwind speed, as long as the glide angle is the same because the thrust is the same. It is true Va = Vg + Vw but if Vg added to Vw does not give always a constant Va, for the same glide angle, then something is wrong with the measurements.
The water speed of a boat traveling upstream depends only on its thrust and is independent of the river speed.
The lift in the table (~62 kg/hp) is quite big in comparison to the lift of the best gliders of the time, mentioned by O. Chanute a few lines below the table, that lifted only 45 kg/hp.
The precise value of the airspeed, Va, is essential in calculating the lift. If ones takes it only 1-2 m/s lower, due to miscalculations, then the evaluated lift grows artificially.

Source: http://gallica.bnf.fr/ark:/12148/bpt6k65534693/f190.item.r=wright
Update
There are a few sources of errors that could have altered substantially the results in the table.
(1) O. Chanute wrote, above the table (see the link), the Wrights did not drift, more than 1/4 in a arc of a circle from the straight line, to always have good headwinds. This drift increases the traveled distance.
(2) The glider was first lifted as a kite to a few meters above the ground with the help of two men. This height made the glide angle to be higher than that of the slope, which can be estimated from a picture (see the attached image where the glide angle appears to be 9.01 deg).
If instead of 7 deg 20' the slope angle was 9.01 deg and the 1902 machine started from a few meters above the ground then instead of 58.1 kg / hp it would have lifted less than 114.4 kg / (114.4 kgf * sin(9 deg 20 minutes) * (54.7 m/12 s + 5.68 m/s) ) = 47.4 kg/hp.
(3) The third factor of incertitude is the wind speed that varies with altitude being stronger a few meters in the air than close to the ground.

Wright glider, 1902. Undated picture.
Question: Do you know a modern replica of the 1902 glider that lifts ~62 kg/hp?
If such a thing exists then the 1902 machine could have lifted 62 kg/hp.

As an open cabin plane of very light weight, the drag from the pilot's body and clothing could vary substantially flight-to-flight based on minor positioning details, so I would not expect that airspeed would be constant for given glide angle and thrust.

Russell Borogove, the drag, D, in kgf (col. 9) is calculated as D = m * sin(a) = Thrust, where a = the glide angle. As you see, D has nothing to do with changes in the position of the pilot or other things as long as the  glide angle is constant. Whatever the pilot does reflects implicitly in the glide angle. As long as a = ct. the pilot induces the same drag.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
Is this a good or a bad propeller?
I want to see if a propeller is bad or good for generating static thrust. This is what I know about the propeller and the engine used to turn it during a test:
Engine shaft power, $P$ = 0.58 hp
Propeller diameter, $D$ = 8.5 ft
Revolutions per minute, $RPM$ = 245
Static thrust, $T$ = 18.75 lbf
Can I calculate the efficiency of the propeller? What is the maximum achievable efficiency?
Additional explanations
The formula I was suggested to use could be exactly what I need. However, using it, I do not get some reported experimental results like:
Engine shaft power, $P$ = 6 hp
Propeller diameter, $D$ = 8.5 ft
Static thrust, $T$ = 66 lbf
Propeller efficiency, $\eta_{prop} \geq 66\%$
Gear efficiency, $\eta_{gears} \geq 85\%$
Doing the calculations: $\eta_{prop} = \sqrt{\frac{T^3}{(P^2 \cdot \pi \cdot \eta_{gears} \cdot \frac{D^2}{2} \cdot \rho )}} = 37.2\%$ which is well below 66%.

Homework question?

It is not homework.

Why the downvotes with no comments?  Seems like a perfectly reasonable aviation question to me.  +1 to help restore CAVOK.

"Bad or good" is opinion.

There is no requirement to provide an explanation for voting, nor should there be.

I do not believe that qualifying a propeller as bad or good is just an opinion. "A well-designed propeller typically has an efficiency of around 80%", (Wikipedia). So, an eff = 37.2% is quite bad.

Honestly, the second propeller (T = 66 lbf) is exactly the one used by the Wright brothers in December 1903. They utilized a 12 hp engine, 2 propellers of diameter D = 8.5 ft and they got a total static thrust T = 132 lbf. According to the brothers the efficiency of both propellers was 66%, a figure nobody had reached before. In reality it appears that the 1903 propellers were below 40% efficient which means the two brothers used in fact bad aerial screws even by the standard of the time.

Engine shaft power: P = 0.58 hp, Propeller diameter: D = 8.5 ft, RPM = 245, Static thrust: T = 18.75 lbf
$\eta_{prop} = \sqrt{\frac{T^3}{(P^2 \cdot \pi \cdot \frac{D^2}{2} \cdot \rho )}} = 49.5\%$
where $\rho=1.2 \frac{kg}{m^3}$
So at an efficiency of 49.5% that propeller is rather poor.
Note: I used the formula that relates static thrust to efficiency, power and propeller diameter from here.

It is known that the efficiency of a plane propeller is low at small forward velocities, so just because eff_prop =~50%, when the plane does not move, it does not mean the propeller efficiency will remain the same as the plane speeds up.


text:
Comparing the Lilienthal and Wright gliders, which one had a better glide ratio?
Where can I find reliable figures about the best glides of Lilienthal and the Wright Brothers (1902 - 1903)?
From the sources below it would appear that Lilienthal's most advanced glider was far superior to that built by the Wright brothers in 1902 as the German apparatus was able to fly 1148 ft while the machine made by the Wrights only 600 ft.
It seems like the wind tunnel tests done by the Wright brothers in 1901-1902 to find optimal wings did not lead to improvements in lowering the glide angle and so increasing the flight distance.
1)"Finally Lilienthal become so skilled that he could make his glides in air velocities of 33 feet per second ... Lilienthal carried out more than 1,000 glides and attained distances of 1,148 ft. at a gliding angle of 4 degree from the hill."
Source: John H. D. Blanke, "Pioneers in Gliding", Popular Aviation, pag. 74 - 77, May 1928
2) "World Record Holders
The improved performance of the 1902 glider finally enabled the Wright brothers to gain extensive practice in the air. During September and October, they made between 700 and 1,000 glides. Flights of 500 feet were common, and a few topped 600 feet. Orville enthusiastically wrote home of their success, “we now hold all records!”"
Source: Inventing a Flying Machine
I'm asking about which glider that had better glide ratio because the Lift/Drag ratio is essential: the higher it is the longer the glide and the less powerful and lighter an engine is needed to make the glider fly horizontally.

could you please define "advanced"?

Airsick , At least one source is unreliable as long as "a few topped 600 feet. Orville enthusiastically wrote home ... “we now hold all records!"" comes into conflict with "Lilienthal ... attained distances of 1,148 ft."".

Raw gliding distance isn't a useful measure of gliding ability.  You also need to take into account launch height and wind velocity.

Otto Lilienthal saw flying as something similar to bicycling: A sport and an opportunity to spend time out in Mother nature. Therefore, he designed all his airplanes such that they would fit through the door of a standard Reichsbahn freight wagon. He used a central truss (Gestellkreuz) to which willow stakes could be bolted such that they would fold backwards. He covered this structure with waxed cotton cloth and used wooden ribs to shape the airfoil of these wings. Consequently, the wingspan of his designs was limited.
The next limitation was his way of controlling his aircraft only by weight shifting. Since his hands were already busy with holding on to the aircraft, he could not use them to move control surfaces. His drawings and his correspondence show that he considered control surfaces and even ailerons, but he did not incorporate them into his designs.
Only his type 18 glider had a rectanguar inner wing which could be pulled close using a scissor link spar. However, with the bigger wing his weight shifting control showed its limits, as this did not lend itself to controlling gliders with bigger wingspans.
Another limit was his insistence that his aircraft would not need a runway or a launching device. Instead, he would grab handles in the Gestellkreuz, stand upright and use his legs as a landing gear. This limited not only the size, but also the wing loading of his designs.
The Wrigths, on the other hand, strived for the mechanically simplest and most lightweight designs and arrived at a biplane of constant chord and much higher aspect ratio. The 1902 glider could already be flown in a prone position and the pilot could control it with control surfaces.

Drag area of the human body in different poses, from Sieghart Hoerner's Fluid Dynamic Drag. The pilot of the Wright flyer caused only one fifth of the drag of the pilot in Lilienthal's designs.
Because the wingspan of the Wright glider was much higher (9.6 m versus 6.7 m for Lilienthal's Normalsegelapparat) and the much higher drag of the pilot's position in case of the Lilienthal design, the Wright glider certainly had a much better glide ratio.

The Lilienthal reference says 4 degree gliding angle from the hill, in air velocities up to 33 feet/second- (presumably wind speed relative to the ground?) Neither reference gives the net change in altitude, and the wind speed, and ground speed at launch, for a specific flight of a particular distance. That's what's needed. From Lilienthal's gliding angle of 4 degrees one could imagine distance to descent ratio of 14.3:1, (slope=1/sin(4 degrees)) but we don't know if the 4 degree slope is in still air, a 33 fps head wind, a 33 fps tail wind, or something else.
("Wait!", you say, "tail wind?" Sure. If distance from launching point is the figure off merit, you'd be a fool NOT to take a tail wind.)
As far as computing glide ratio, the raw facts aren't here to compute it with certainty for either glider.  And slope lift (air driven upward by hitting terrain) ought to at least be checked if not factored in, as well.
Its possible that a comprehensive table of air foils from the early days might have both the final glider airfoils for the Wrights and Lilienthal. And those air foils would have L/D ratios, but those are NOT the same as the gliding ratios of actual airplanes. The performance of the vehicles included not just the wing L/D but the parasitic drag of the whole structure and the wing loading. Which brings us back to the height of the descent and the distance covered.